Abstract

An analytical method and associated algorithms for calculating the collection efficiency of a spectrograph for distributed sources are presented. The method is useful for optimization studies and for estimating calibration parameters without resorting to Monte Carlo or other sophisticated radiation transport methods.

© 1983 Optical Society of America

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References

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  1. J. R. Nielsen, J. Opt. Soc. Am. 20, 701 (1930).
    [CrossRef]
  2. J. R. Nielsen, J. Opt. Soc. Am. 37, 494 (1947).
    [CrossRef] [PubMed]

1947

1930

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Figures (6)

Fig. 1
Fig. 1

Expanded view of the spectroscopic setup.

Fig. 2
Fig. 2

View of the effective regions in the x-y plane.

Fig. 3
Fig. 3

Effective angle for region I in the x-y plane.

Fig. 4
Fig. 4

Effective angle for region II in the x-y plane.

Fig. 5
Fig. 5

Effective angle for region III in the x-y plane.

Fig. 6
Fig. 6

Effective angle for region IV in the x-y plane.

Tables (1)

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Table I Region Selection Criteria

Equations (4)

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Δ Ω ( x , y , z ) Δ θ ( x , y ) Δ θ ( x , z ) .
P ( x , y , z ) = Δ Ω ( x , y , z ) 4 π .
I Δ θ ( x , y ) = tan - 1 ( a / 2 - y s - x ) + tan - 1 ( a / 2 + y s - x ) , II Δ θ ( x , y ) = tan - 1 ( w / 2 - y x ) + tan - 1 ( w / 2 + y x ) , III Δ θ ( x , y ) = tan - 1 ( a / 2 - y s - x ) + tan - 1 ( W / 2 - y x ) , IV Δ θ ( x , y ) = tan - 1 ( w / 2 - y - x ) + tan - 1 ( a / 2 + y s - x ) .
Δ Ω ( x , y , z ) = | 4 tan - 1 cos 1 2 [ Δ θ ( x , y ) - Δ θ ( x , z ) ] cos 1 2 [ Δ θ ( x , y ) + Δ θ ( x , z ) ] - π | .

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